Wireless communication systems may use spatial multiplexing techniques wherein a single transmitter simultaneously emits multiple information signals, each of which is intended for one of a number of spatially separated receivers. The directional properties of transmitting antenna arrays are exploited in such systems to generate a beampattern for each signal which is directed towards its intended receiver. For example, such transmitting arrays are used in satellites to beam different signals to different receiving locations.
By adjusting the amplitude and phase at which a signal is applied to the elements of the transmitting array, the gain of the signal can be maximized in the direction of its intended receiver and minimized in the directions corresponding to other receivers. Where sufficient information is available about the transmission channels between the transmitting array and each receiver, a complimentary null beampattern can be generated for each signal. Such a beampattern has unit gain in the direction of the intended receiver and zero gain in the directions of all other receivers.
A frequent problem with such systems is that the information available about the propagation environment is insufficient to produce the desired beampattern. Uncertainties in the response of the transmitting antenna array, the locations of the intended receivers, and the nature and location of scatterers in the vicinity of the array, limit the information available about the transmission channel. In such cases, the beampattern formed has non-zero gain in the direction of unintended receivers, leading to cross-talk among signals. Cross-talk degrades the quality of the signal at its intended receiver, and in the worst case, may wash it out altogether.